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If I understand the question correctly, you are asking whether it's really needed to have the KEM be CCA secure, and maybe in the random oracle model it would suffice for it to just be an invertible one-way function.
This would not be CCA2-secure. Specifically, let $f$ be any invertible one-way function, and construct $f'$ so that $f'(x)=0f(x)$ for every ...

It can be proved, mathematically, that your (2), (3), and (4) are all equivalent under chosen plaintext attack. That is, if you can do any of those things then you can also do the other two!
It should be obvious that (2) implies both (3) and (4): if you can decrypt a message then you know which message it is, and also you know it's not random noise.
The ...

This isn't really a "hard" answer, but an attempt to give some intuition or motivation.
One can interpret indistinguishability as an overapproximation of the most common notions of security: Any system that is broken in a more practical way will also fail to meet indistinguishability, that is, all practically important security requirements are in fact ...

Katz & Lindell mention in their book "Introduction to Modern Cryptography: Principles and Protocols" an example of an IND-CPA attack from World War II.
Navy cryptanalysts suspected that Japanese ciphertexts containing the fragment "AF" where referring to the Midway island. Then, they told officials at Midway to send unencrypted messages reporting they ...

The CCA1 security of ElGamal is a big open question. There are no attacks known, but standard reductions don't seem to work.
In 1991, Damgard proposed an ElGamal variant and proved it to be CCA1-secure (albeit under a very problematic non-falsifiable assumption, called the "knowledge of exponent assumption"); see the paper here ...

As already mentioned in a previous answer and the comments, you are right regarding that ElGamal is not secure against chosen-ciphertext attacks. An immediate reason is that the scheme is multiplicatively homomorphic, and that is not compatible with CCA: the attacker could query the decryption oracle with the ciphertext that results of multiplying the ...

The ideal encryption scheme $E$ would be one that, for every ciphertext $C=E(K, M)$, if the key remains secret for the adversary, the probability of identifying $M$ is negligible. Since that is not possible in practice, the second most reasonable approach is to define constraints strong enough to satisfy some definition of security. The $IND-$ notation ...